Effects of Practical Rechargeability Constraints
on Perpetual RF Harvesting Sensor
Network Operation
DEEPAK MISHRA, (Student Member, IEEE), AND SWADES DE, (Senior Member, IEEE)
Department of Electrical Engineering, and Bharti School of Telecommunication, IIT Delhi, New Delhi, Delhi 110016, India Corresponding author: S. De (swadesd@ee.iitd.ac.in)
This work was supported by the Department of Science and Technology under Grant SB/S3/EECE/0248/2014.
ABSTRACT Green perpetual sensor network operation is the need of the hour for critical applications, such as surveillance, military, and environment monitoring. Mobile integrated data collection and recharging is a promising approach to meet this requirement by routinely visiting the field nodes for collecting the sensed data and supplying energy via radio frequency (RF) energy transfer. Practical constraints, such as self-discharge and aging effects of the energy storage element (supercapacitor), significantly impact the renewable energy cycle (REC) and, hence, strongly influence the performance of RF energy harvesting networks. To account for the nonidealities in practical supercapacitors, in this paper, a circuit model for REC is proposed, and corresponding RF charging time and node lifetime expressions are derived. Hardware experiments are performed to validate the proposed REC model. REC for complicated supercapacitor models is characterized using duality principle and a generic simulation model. Using the developed analytical models for practical supercapacitors, the size of network for perpetual operation is estimated, which is demonstrated to be significantly less than that predicted by considering ideal supercapacitor behavior. For example, with three-branch supercapacitor model, the estimated sustainable network size is shown to be nearly 52% less than that offered by the ideal supercapacitor model.
INDEX TERMS Charging time characterization, integrated data collection and recharging, practical supercapacitor models, radio frequency energy transfer, renewable energy cycle.
I. INTRODUCTION
Wireless Sensor Networks (WSNs) have wide range of applications, such as, environment monitoring and surveillance [1], [2]. However, finite on-board energy of the senor nodes limits its widespread usage. Energy harvesting and wireless power transfer (WPT) offer the potential to green perpetual network operation. Radio frequency (RF) energy harvesting (RFEH) from ambient sources is such an energy refilling approach that addresses the carbon footprint concerns. Unlike the other harvesting techniques [3], RF energy transfer (RFET) from dedicated source(s) provides more controlled operation and enables energy sharing among rechargeable devices.
Efficient data collection from the field sensors is another important aspect in WSNs. Traditional methods suffer from two major problems. First, direct data transfer to a remote sink may consume excessive battery energy of field nodes due to super-linear path loss. Second, even if multi-hop techniques are adopted, the network may suffer
from hot-spot problem [4], where the nodes closer to the sink deplete energy at a faster rate because of handling higher volume of relayed traffic. To this end, in mobility-assisted schemes [5], the mobile data collectors with controlled mobil-ity visit the field nodes to collect data that saves energy and provide balanced energy depletion. To achieve uninter-rupted network operation, we consider the existence of an optimal tour of a mobile robot which visits the field nodes routinely to collect the field data and replenish the drained energy via dedicated RFET. Extending the concept of con-ventional data mobile ubiquitous LAN extensions (MULE), such a mobile robot acts as an integrated data and energy MULE (iDEM) [6].
A. MOTIVATION
Integrated data collection and recharging using iDEM for perpetual network operation involves a renewable energy cycle (REC), where the amount of energy stored at a field node must be at least equal to the energy consumed during 2169-3536 2016 IEEE. Translations and content mining are permitted for academic research only.
discharge phase of the cycle. So, REC has two phases: a) charging, b) discharging (see Fig. 1). Charging is done via RFET from iDEM. Discharging phase involves drainage of the stored energy for carrying out various field node operations. To quantify the efficiency of iDEM-powered WSNs, recharging process as well as leakage of the node’s energy storage element (supercapacitor) need to be charac-terized. Practical supercapacitor models are more complex than the ideal ones due to the nonidealities like self-discharge, leakage current, and aging effects. So, consideration of prac-tical supercapacitor characteristics is very crucial in iDEM path planning for a realistic estimate of perpetual network operation.
FIGURE 1. Renewable energy cycle. The charging and discharging cycles represent the voltage across the supercapacitor with capacity C = 50F, charging DC power P = 25mW, and loading power Pconsavg =2.8mW. This figure is plotted by using the equations for charging and discharging time derived later in Sections IV-Aand IV-B, respectively.
B. KEY CONTRIBUTIONS
Objective of this paper is to estimate the sustainable network size using iDEM, for perpetual operation of energy-hungry field sensor nodes that are operated by practical recharge-able supercapacitors. Key contributions of this work are as follows:
i) Practical REC circuit model is proposed along with its analytical characterization and experimental validation.
ii) Analytical RF charging time equations are developed for the practical supercapacitor models.
iii) Based on a novel duality principle, constant-power loading time of field nodes is characterized using RF charging equations. This behavior is experimentally validated.
iv) A reliable simulation model is developed that closely approximates the charging and loading behaviors of the analytically-intractable, practical supercapacitor models.
v) The developed loading models are used to estimate the node lifetime of practical wireless field sensor nodes. vi) From the estimated (potentially random) node lifetime
and RF charging time characteristics, sustainable net-work size supported by a single iDEM is obtained. C. PAPER ORGANIZATION
Prior art is surveyed in Section II. The proposed REC circuit model and its role in perpetual network
operation are discussed in Section III. Analytical characteri-zation of RF charging time and duality principle establishing a relationship between constant-power charging and loading times are presented in Section IV. REC circuit model is experimentally validated in Section V. A generic simulation model is developed in Section VI for characterizing REC with advanced supercapacitor models. Sustainable network size supported by a single iDEM is evaluated in Section VII. Section VIII concludes the paper.
II. RELATED WORK
WIRELESS POWER TRANSFER
WPT can be classified in two main categories [7]: (i) non-radiative techniques which include inductive cou-pling and magnetic resonance coucou-pling, and (ii) electro-magnetic radiation based schemes which include RF waves, microwaves, and light waves. Periodic replenishment of the nodes’ battery energy via non-radiative WPT was considered in [8]. The application of RFET for prolonging lifetime of rechargeable WSNs has been discussed in [6], [9]–[11].
Recently, there has been a growing attention towards improving RFET efficiency for realizing uninterrupted oper-ation of WSNs [12]. With the advancement in RF harvest-ing circuit designs [13], smart cooperative energy sharharvest-ing schemes [14], [15], and multi-antenna based energy beam-forming technologies [16], the gains achieved from dedicated RFET have significantly increased. However for practical realization of perpetual WSN operation, hardware constraints involved in charging and discharging of RF-powered nodes needs to be accurately characterized [17].
CHARGING AND LOADING TIME CHARACTERIZATION In a recent study [18], RFET has been shown to provide constant-power charging of the on-board supercapacitor. This work also developed RF charging equations for series RC circuit based supercapacitor model. The energy consumption models of wireless sensor node are provided in [19]–[21]. The studies in [22] and [23] assumed the field node to be a constant-power load that is powered by the energy stored in the supercapacitor. Constant-power loading equations for series RC circuit are provided in [24] and [25]. The simplified models developed in [18] and [22]–[25] provide valuable insights on charging and loading process. However, our experimental observations suggest that, practi-cal supercapacitors require more elaborate considerations for accurate characterization of charging and loading process. PRACTICAL SUPERCAPACITOR MODELS
Leakage and aging of the on-board supercapacitor are the two major practical aspects to be accounted, as they have significant impact on the energy harvesting network performance. In the existing works, supercapacitor has been modeled considering ideal capacitor [23], or series RC circuit [18], or a simplified equivalent circuit with series and parallel resistances to account the short-term leakage effects [26]. The non-ideal characteristics of supercapacitor
is due to its internal construction [26], which is different from that of a regular capacitor. Most popular supercapacitor model which accounts the long term behavior was presented in [27]. This model was extended in [28] to represent the behavior of supercapacitors at both low and high frequencies. An accurate modeling of dynamic diffusion phenomenon of supercapacitor residual charge during charging/discharging and rest phases was proposed in [29]. Although the prior works [23], [26]–[29] considered supercapacitor models with different degrees of complexity, analytical characterization of charging and loading times, required for energy harvesting network performance evaluation, is missing in the literature.
INTEGRATED DATA COLLECTION AND RECHARGING
Mobile platform for data collection and recharging was presented in [30] to minimize overall network energy consumption. Non-radiative energy transfer based joint optimization of effective charging and data collection was recently studied in [31]. In another non-radiative approach [32], network utility maximization problem under flow conservation, energy balance, and link capacity con-straints was studied. The above works leave scopes on accounting varying energy consumption of the nodes [33] and dynamic data collection requirements [5], which would bring up additional challenges of on-demand iDEM service.
In the current work, we use radiative RFET because it does not have the strict constraints of distance, inter-node alignment or resonant coupling. Rather, it has the beam steer-ing capability to enhance energy transfer gains [15] and pro-vides simultaneous recharging of multiple nodes [17]. Also, it enables joint energy and field data transfer over the same RF signal.
III. PROPOSED CIRCUIT MODEL FOR REC CHARACTERIZATION IN PERPETUAL NETWORK OPERATION
A. RENEWABLE ENERGY CYCLE CIRCUIT MODEL
For perpetual network operation, remaining energy at each rechargeable node must follow a cycle, which is defined below:
Definition 1: Energy stored in the supercapacitor follows renewable energy cycle (REC)with periodτrecif the energy
consumption Econsduringτrecis at most equal to the energy
stored Estored in the supercapacitor at the beginning of the
cycle, and thus the energy level never falls below the min-imum required energy level Emin. Emin takes care of the
energy required for sending the field node’s data to the iDEM. Mathematically, Econs ≤ Estored = Esupp − Elost, where Esupp = PTC is the DC energy (P is the DC power, TC is
the charging time) available at the field node through RFET, and Elost is the energy lost due to leakage and aging effects.
We present circuit models for REC characterization, as shown in Fig. 2, which comprise of constant-power charging and loading of practical supercapacitor models. In Fig. 2(a), the DC power P available after RF-to-DC conversion by
FIGURE 2. Proposed REC (charging + loading) circuit model. (a) Constant-power charging. (b) Constant-power loading.
P1110 IC [34] is modeled as constant power source with VOUT = V(t) as the source voltage and I (t) as the source
current [18]. In Fig. 2(b), a field node having DC-DC con-verter is modeled as a constant-power load operated by the energy stored in the supercapacitor, with I (t) as the loading current.
B. ROLE OF REC IN PERPETUAL NETWORK OPERATION Here we first discuss preliminaries of the application network considered, followed by the role of accurate REC characteri-zation in analyzing the feasibility of its perpetual operation. 1) NETWORK MODEL
We have considered a pollution monitoring WSN with static field nodes N deployed in the field following Poisson point process. dijis the Euclidean distance between the nodes i and j
(i, j ∈ N ). Each node consists of: a) one or more toxic gas sensors, b) memory card for data storage, c) low-power micro-controller, d) energy harvesting unit, e) commu-nication module, f) passive wake-up radio module, and g) an on-board supercapacitor. We have used (i) Alphasense gas sensors [20] for sensing CO, H2S, SO2, and NO2, which generate current proportional to the toxicity level; (ii) Powercast P1110 [34] for RFEH; and (iii) Mica2 mote for data processing, storage, and communicating with the iDEM. 2) STATE-DEPENDENT CONSUMPTIONS
Energy consumption of a field node depends on its opera-tion states (Fig. 3(a)). It senses the pollutant(s) at a rate sr
(samples/day). The CPU is periodically activated from sleep state to store the sensed data. The sensing duty cycle is: DC = Ns/nsr(trt+tw)
d , where Ns/n, tr, tw are respectively the
FIGURE 3. Application network model. (a) State diagram for node’s operation. (b) iDEM scheduling.
number of sensors per node, sensor response time, and data logging time. Day duration td = 86400 sec. Upon arrival,
the iDEM transmits a wake-up signal [35] to the field node. On receiving the wake-up signal, the node’s CPU transits from sleep to active state and the radio switches to receive mode. Subsequently, on receiving a ‘‘hello’’ signal from iDEM, the node transits to transmit mode to send the status of remaining energy and collected data to the iDEM. This two-way handshake leads to data transmission, followed by RFET from the iDEM. For efficient WSN operation, we assume that the sensor node continues to perform its regular periodic operations (as mentioned in Fig. 3(a)) even during the RFET process because RF charging time may be high depending upon the capacitor size and node’s remaining energy. Using the current consumption during different operation states at supply voltage Vop =3 V and the time spent in each state,
given in Table 1, the average power consumption Pavgcons= VopIconsavg of a field node is calculated as:
Pavgcons = 3 × td to+ td DC(trIse+ twIw) tr + tw +(1−DC) Isl + 3toIo to+td (1) where to and Io are respectively the time spent and
cur-rent consumption during communication and radio transition operation, which are performed only when the iDEM visits the node. Ise, Iw, and Isl are current consumption during
sensing, data logging, and sleep state.
TABLE 1. Current consumption in different states.
C. IDEM SCHEDULING AND IMPORTANCE OF REC Given a renewable energy cycle along with a network model, iDEM scheduling problemis defined below:
Definition 2: Design an optimal revisit schedule for the iDEMso that it can serve the maximum number of nodes without letting the remaining energy of any node reduce below the threshold Emin, in minimum possible cycle time.
The iDEM starts from a service station (home) and is assumed to have sufficient energy to carry out its services before returning to home (cf. Fig. 3(c)). Depending on the energy consumption of a node, it may require multiple iDEM visits in a single period of schedule. The optimal iDEM schedule depends on iDEM revisit time at each node, which itself depends on three parameters1: a) RF charging time, b) loading time which is a function of Pavgcons, and c) inter-node
distances. As the inter-node distances are known and can be used to design the optimal schedule, our goal is to present ana-lytical insights, backed by simulation and numerical results, on the charging and loading times for practical supercapacitor models.
IV. THEORETICAL ANALYSIS OF REC CIRCUIT MODEL
In this section we provide an analytical characterization of recharging cycle (or REC) for different supercapacitor models.
A. ANALYTICAL CHARACTERIZATION OF CHARGING TIME First, we formally define RF charging time as follows:
Definition 3: RF charging time TCis defined as the time
required to charge a supercapacitor from some initial voltage VC= VL to a fully-charged state with VC = VH.
As the voltage VC across the supercapacitor is a function of time, we use VC and VC(t) interchangeably without any difference in meaning. Now, we will derive the RF charging time equations for different supercapacitor models.
1) IDEAL MODEL
Here, supercapacitor is treated as a conventional capacitor. From Fig. 4(a), P = V (t) · I (t) = Cq · dq
dt. Using q = CVC and solving for VC we obtain voltage VC(t) across an initially uncharged supercapacitor at any time t,
Z VC 0 VCdVC = Z t 0 P Cdt or, VC(t) = r 2Pt C . (2) From (2), current variation with time is obtained as I(t) = q PC 2t. RF charging time T ideal C for storing Q
Coulombs of charge or VC(t = TCideal) , VH across an initially-uncharged supercapacitor (VC(t = 0), VL =0 V) is given by: TCideal(VH) = C P Z VH 0 VCdVC =CV 2 H 2P . (3)
1Data collection time is neglected, as it is very small [5] compared to RF charging time and also the field nodes are equipped with enough memory capacity for storing data over reasonably-long iDEM revisit interval.
FIGURE 4. Supercapacitor models. (a) Ideal model [23]. (b) Commercial model [18]. (c) Simplified model [26]. (d) 1-branch model [27]. (e) Practical 3-branch model [27].
2) COMMERCIAL MODEL
This is the most commonly used and commercially adopted model of the supercapacitor which consists of a capaci-tor with an equivalent series resistance (ESR) R. Applying Kirchhoff’s voltage law (KVL) in Fig. 4(b) we have, P = V(t) · I (t) =VR(t) + VC(t) · I (t) = R · dq dt 2 +q C· dq dt.
Substituting q = CVC and solving the resultant quadratic equation in dVC
dt to find the time T com
C to charge an initially
uncharged (VL =0) supercapacitor to voltage VH, we obtain,
TCcom = RC 2 2VH q V2 H +4RP − VH +ln q V2 H +4RP + VH q V2 H +4RP − VH (4) The voltage across the capacitor at time t is:
VC(t) = 2 √ RP1 − Z1 r 1 −1 −Z12 , with Z =1 2 h 1+W0 e1+RC2t i (5) where W0(·) is the Lambert function (principal branch) [18]. The current across capacitor at time t is given as:
I(t) = CdVC dt = −VC(t) + r h VC(t)2+4RPi 2R . (6) 3) SIMPLIFIED MODEL
It consists of a capacitor with an ESR RS and an equivalent parallel resistance (EPR) RP and accounts for the short-term
leakage effects. Applying KVL in Fig. 4(c), P = V(t) · I (t) = h I(t) · RS + IR P(t) · RP i · I(t). (7) I(t) in terms of VC(t) is obtained using Kirchhoff’s current law (KCL) at node (k) in Fig. 4(c) as: I (t) = VC(t)
RP + CdVC(t) dt . Substituting in (7) gives P = V C RP + C dVC dt 2 RS + VC V C RP + C dVC dt , quadratic in VC RP + C dVC dt , with solution: VC RP + C dVC dt = −VC+ q V2 C+4RSP 2RS . (8)
Solving (8) to find time TCsimprequired to charge an initially uncharged (VL =0) supercapacitor to voltage VH, we obtain,
TCsimp = RPC 4(RP+ RS) RPln 4RSP q V2 H +4RSP + VH 2 +(RP +2RS) ln R 2 PP R2 PP − V 2 H(RP+ RS) ! +2(RP+2RS) tanh−1 VH(RP+2RS) RP q V2 H +4RSP . (9) Intuitively, TCsimpis a function of VL and VH.
Similarly, by using dIRP dt = 1 RPC I(t) − IR P(t) and solv-ing (7) for I (t), the time TCsimp
Tpr1b C = 1 4 ( 2CvRle 2 √ Y −q4Y + V2 H −2CvVH(2R1+ Rle) + C1(2R1+ Rle) ln " PRle PRle−VH2 # +(2R1+ Rle) " ln " 4√PRleR1(R1+Rle)+2Rle(2R1+Rle) √ Y√PRle+VH Rle 2R1 q 4Y +V2 H+Rle q 4Y +V2 H−VH +4√PRleR1(R1+Rle) #! × C1− Cv √ PRle + ln " Rle 2R1 q 4Y +V2 H+Rle q 4Y +V2 H+VH +4√PRleR1(R1+Rle) 4√PRleR1(R1+Rle)+2Rle(2R1+Rle) √ Y√PRle−VH #! × C1+ Cv √ PRle + Cv √ PRle 2 tanh−1h√VH PRle i +ln [PRle]i+ C1Rleln " 4Y q 4Y +V2 H+VH 2 #) . (13) I(t) falls IH = I(t = 0) =qRP S to IL = I TCsimp I , is: TCsimp I = RPC (RP +2RS) ln " PRP RSI2 L(RP+RS)−P # 2(RP + RS) −ln 1 IL s P RS !# . (10)
4) PRACTICAL 1-BRANCH MODEL
To reflect the voltage dependence of capacitance, this model consists of a voltage-dependent differential capacitor comprising a fixed capacitance C1 with parallel voltage-dependent capacitance Cv. Apart from series resistance R1, a leakage resistor Rle, parallel to differential capacitor, is
added to represent self discharge property. Applying KVL in Fig. 4(d), V(t) = VR1(t) + VC(t) = C1+CvVC(t) dVC dt R1+VC(t). (11) Using P = V (t) V R1(t) R1 + V R1(t)+VC(t) Rle in (11) gives: C1+ CvVC dVC dt = −VC1 +2R1 Rle 2 R1+ R21 Rle + s h VC 1 + 2R1 Rle i2 +4 P −V 2 C Rle R1+ R 2 1 Rle 2 R1+ R 2 1 Rle . (12) Solving (12), the time Tpr1b
C required to charge an initially
uncharged supercapacitor (VL = 0) to maximum voltage VH, is given by (13), as shown at the top of this page. where Y = PR1(R1+Rle)
Rle .
Note that, (13) is quite complicated, which hints analytical intractability of more realistic models. Temporal variation of charging current is given in Appendix A.
5) PRACTICAL 3-BRANCH MODEL
This is the most comprehensive model [27], that provides the desired insight into the complex terminal behavior of the supercapacitor. To account for the long-term behavior, apart from parallel leakage resistance Rle, it consists of
three branches: a) first or immediate branch, with differen-tial capacitor (fixed capacitance C1 with parallel voltage-dependent capacitance Cv) and series resistance R1, domi-nates immediate behavior of the supercapacitor in the range of seconds in response to a charge action; b) second or delayed branch has capacitance C2 in series with resis-tance R2, that dominates the terminal behavior in the range of minutes; c) third or long-term branch has capacitance C3in series with resistance R3, determining the behavior for times longer than 10 min. Applying KCL in Fig. 4(e),
Ij(t) =V (t) − VCj(t) Gj∀j ∈ {1, 2, 3} , IRle(t) = V (t)Gle (14) Using (14) and I (t) = 3 P j=1 Ij(t) + IRle(t), we obtain: P =(V (t))2 3 X j=1 Gj+ Gle −V(t) 3 X j=1 VCj(t)Gj . (15) (15) is quadratic with V (t) as the unknown. Its solution is:
V(t) = 1 2 3 X j=1 Gj+ Gle 3 X j=1 GjVCj(t) + v u u u t4P 3 X j=1 Gj+ Gle + 3 X j=1 GjVCj(t) 2 (16) where G1, G2, G3, and Gle are the conductances, given by, Gj= R1
j∀j ∈ {1, 2, 3}, and Gle= 1
Rle. Using (14) and (16), the state-space equations representing the behavior of variation of voltage across capacitors in different branches are given as:
C1+ Cv· VC1(t)
dVC1(t)
FIGURE 5. Analytical model for constant-power loading (CPL). (a) CPL of commercial model. (b) CPL of simplified model.
=V (t) − VC 1(t) G1 (17) Cj dVCj(t) dt =V (t) − VCj(t) Gj, ∀j ∈ {2, 3} . (18) V(t) in (17) and (18) is a function of VC1(t), VC2(t), and VC3(t), as given in (16). The given system of state-space equations is quite complicated and contains nonlinear terms, due to which it cannot be solved analyti-cally. Moreover, further complex supercapacitor models have been proposed recently [28], [29], which are even more complicated and advanced than the above-discussed 3-branch model. To address these upcoming models, for which explicit analytical RF charging equations cannot be derived, we propose an generic and versatile simulation model in Section VI.
B. ANALYTICAL CHARACTERIZATION OF NODE LIFETIME Lifetime of a node is defined as follows:
Definition 4: Lifetime Tlifeof a node is the time for which
it can carry out its operation from the energy stored in its supercapacitor, or in other words, the remaining energy level for t > Tlifefalls below Eminand the node lifetime expires.
So, for continuous operation of the field node, iDEM revisit time should be less than Tlife. As mentioned in Section III-A, the DC-DC converter provides constant voltage to the load circuitry (i.e., the field node comprising of a processor and sensing circuits). So, as the voltage across the supercapaci-tor decreases with drained energy, the current consumption increases to maintain a constant voltage level for the node’s proper operation. Thus, the wireless field node acts as a constant-power load. It may be noted that, due to high effi-ciency ξDC−DC of DC-DC converters in commercial motes (e.g., ξDC−DC > 90% in [36]), we assume that the power P drawn by the sensor node is equal to its actual aver-age consumption Pavgcons. However, in general P = P
avg cons ξDC−DC
. Before we present a novel duality principle that will be used for deriving constant-power loading (CPL) time expres-sions, we define loading time and provide its relationship with Tlife.
Definition 5: Loading time TL is the time interval
dur-ing which the voltage across a fully charged capacitor drops from VH to VL. If VL corresponds to the minimum-required energy Eminin field node for its continued operation,
then Tlife= TL.
1) DUALITY PRINCIPLE
Here we investigate an interesting relationship between the RF (or constant-power) charging and CPL time, that can be noted from Fig. 4(b) (or 4(c)) and Fig. 5(a) (or 5(b)). In particular, we demonstrate a duality relationship between the time required to charge a supercapacitor with capaci-tance C from an initial voltage VL to a threshold voltage VH using RF charging and the time required to discharge the supercapacitor from VH to VL using a constant-power load. Duality can be explained with the help of Figs. 2(a) and 2(b), where it is shown that the RF charging and constant power loading have a reciprocal relationship:
• The direction of current and power flow with respect to the supercapacitor are reversed (cf. Figs. 2(a) and 2(b)). • The initial and final voltage/current levels are opposite. Theorem 1: Duality principle implies that TL can be obtained from TC, and vice versa, by applying following rules:
Charging time TC ←→ Loading time TL; P ←→ −P;
VL to VH or, IH to IL ←→ VH to VL or, IL to IH. (19) Proof: Duality can be proved by first deriving CPL time expression for any supercapacitor model (without loss of generality) and then showing how applying duality rules to it gives the corresponding RF charging time equation derived in Section IV-A. We derive TL expression for
com-mercial model. On applying KVL and using P = V (t) · I (t) in Fig. 5(a), P =VC(t) − VR(t) I (t) = −CVC dVC dt − RC 2 dVC dt 2 . (20) The solution of (20) is:dVC
dt = VC−
q
VC2−4RP
2RC . Solving for the loading time t = TLcom, after which a fully-charged super-capacitor (with VC(t = 0) = VH) is drained to VC(T
com L ) = VL (corresponding to Emin), we obtain:
TLcom = Tloadcom(VL) − Tloadcom(VH), with Tloadcom(VC) = C 4RP h ln ˆ A i − VCAˆ 4P (21) where ˆA = q VC2−4RP + VC
. Note that, (21) providing TLcomas a function of VLand VH is valid only for VL ≥
√ 4RP. Applying duality rules (19) in (21), with VL =0:
TC = RCln q VH2+4RP + VH 2 √ RP + CVH q VH2 +4RP + VH 4P (22)
2) LOADING TIME EXPRESSIONS
Following Theorem 1, CPL time equation for a supercapaci-tor model can be obtained from its corresponding RF charging time expression. It may be noted that CPL time expres-sions for simplified and 1-branch models respectively are valid only for VL ≥ max
( p4RSP, r R2 PP (RP+RS) ) and VL ≥ r Rle 4P R1Rle+R21 2(2R1+Rle)2−R21
. Interestingly, the loading time TLidealfor ideal model is, TLideal(VH, VL) = CV
2 L −2P− CV2 H −2P = CV2 H 2P − CV2 L 2P = TCideal(VL, VH).
Similar to temporal variation of voltage, relationship between loading current and CPL lime can be obtained using the duality rules. For example, using duality rules and TCsimp
I expression given by (10), time TLsimp
I , during which the energy stored in a fully charged supercapacitor (simplified model) VC(t = 0) = VH reduces to Emin, or loading current I
increases from IL = VH −qV2 H−4RSP 2RS to I (t = T simp LI ) = IH is given as: TLsimp
I = T simp Iload(IH) − T simp Iload(IL), where T simp Iload(I ) = RPC ln(I) −(RP+2RS) ln −P−I 2R S+RP 2(R P+RS) . V. EXPERIMENTAL VALIDATION
Here we experimentally validate the assumptions in the anal-ysis of renewable energy cycle.
A. RF CHARGING PROCESS AND PRACTICAL SUPERCAPACITOR MODEL PARAMETER ESTIMATION RF charging as a constant-power charging process has been experimentally validated with commercial 50 mF superca-pacitor in our recent work [18]. The circuit model parameters of the two supercapacitors 4.7 F and 50 F, given in Table 2 and used later in our simulations have been experimentally validated in [26] and [37], respectively.
TABLE 2. Circuit model parameters [26], [37].
B. CONSTANT-POWER LOADING
We have undertaken systematic experiments to validate the CPL behavior of the field node, as assumed in Sections IV-B. We have used Libelium Waspmote PRO V1.2 [38] and measured its consumption during the sensing state with toxic gas sensors CO and NO2. The experimental setup (Fig. 6(a)) comprises of: i) wireless field node (Waspmote, Gas Sensors:
FIGURE 6. Experimental validation of constant-power loading process. (a) Experimental set up. (b) NO2gas sensor. (c) CO gas sensor.
MiCS-2710 (NO2), TGS2442 (CO), communication module: Digi XBee Series 2, 2.4 GHz 5 dBi antenna, 2 GB microSD memory card); ii) DC voltage supply (Instek GPD-3303S); iii) multi-meter (HP34401A); iv) a low-value resistor (0.18). DC supply, wireless node, and resistor are connected in series, while the multi-meter is connected in parallel to the resistor for measuring voltage. Low-value resistor is used to find the current consumed by the node without causing loading effect. The supply is varied from 3.3 V to 4.2 V (operational range).
The measured current consumption readings plotted in Figs. 6(b) and 6(c) for field node in active state include the consumption of processing module (≈ 15 mA), gases board, gas sensors, memory, but not the consumption of the com-munication module as it is disabled during sensing. Also, the current readings plotted are the average consumptions during the typical response duration of each sensor: 30 sec for NO2 sensor and 1 sec for CO sensor [38]. The current readings are calculated by averaging the recorded V0.18
0.18
readings for each supply voltage value. The plots also show that the current drawn by the Waspmote decreases with increasing supply voltage.
Power consumption of the Waspmote for each sensor dur-ing the active state is obtained by multiplydur-ing the supply volt-age with the corresponding current consumption. The power consumption values are also plotted in Figs. 6(b) and 6(c) along with its zero-degree polynomial (constant function) fit. The normalized percentage change in the measured powers with respect to their mean (or poly-fit) values are respec-tively 0.21 and 0.41 for NO2 and CO gases. The results show that, the power consumption during active state of the Waspmote for monitoring both the gases can be very closely approximated by a constant function, thereby validating the CPL behavior.
C. VALIDATION OF THE PROPOSED REC CIRCUIT MODEL Here, to validate the proposed REC circuit model, we present the measurement results for charging and discharging of 40 F Lithium-ion capacitor LIC-1235R-3R8406 with
FIGURE 7. Experimental results for charging and discharging cycle in commercial supercapacitor model. (a) Experimental set up. (b) Measurement circuit. (c) Charging voltage variation. (d) Loading voltage variation. (e) Loading current variation.
ESR = 0.15 (considering commercial supercapacitor model).
The experimental setup is shown in Fig. 7(a). It consists of three main components: (i) the RF source, which is a Powercast transmitter [34] placed 45 cm away from the end node and transmits with Effective Isotropic Radiated Power (EIRP) = 3 W at 915 MHz; (ii) the wireless field node, which includes Powercast P1110 RFEH circuit and 40 F supercapacitor, in addition to the basic components as indicated in Section V-B; (iii) the measurement circuit com-prising of a digital oscilloscope (Tektronix TDS 2024B), multi-meter (Agilent 34405A), laptop (for recording measurements using NI LabVIEW), breadboard, and a low-value precision resistor (0.18 ). The measurement circuits for charging and discharging operations are shown in Fig. 7(b). For wireless charging of the node, the RF source transmits at 3 W, until the supercapacitor voltage reaches 3.8 V (maximum usable voltage). With path loss exponent taken as 2 (which is true for short transmitter-receiver dis-tance), the received RF power is 41.03 mW. This yields an RF-to-DC rectification efficiency of 72.4% [34] and har-vested DC power as P = 29.70 mW. The measured variation of capacitor voltage along with the analytical results obtained from Section IV-A.2 with P = 29.70 mW, C = 40 F, R = 0.15 is plotted in Fig. 7(c). It is observed that the analytical results for commercial model closely match with experimental results – thereby validating the constant-power charging analysis. As noted in [26] and [27], more closer match of the analytical results with the measured values are expected for practical supercapacitor models that incorporate the nonidealities attributed to substantial leakage currents.
The capacitor voltage and loading current (individual state current consumption for Waspmote) results for discharging cycle are presented in Fig. 7(d) and 7(e), respectively. The measured results are obtained over three cycles, each com-prising of a sleep state (10 sec), followed by CO and NO2
sensingwith respective response duration of 1 sec and 30 sec. The sensed readings are stored in the SD card during the loggingstate. Fig. 7(d) plots the variation of capacitor voltage with time. The experimental results are based on the instan-taneous values, whereas the analytical results for commercial model are based on the average power consumption of the field node. The results show a close match between ana-lytical and experimental readings – thereby validating CPL assumption. However, as discussed in Section IV and shown later in Section VI, practical models offer much better match by incorporating the nonidealities attributed to supercapac-itor charging and discharging behaviors. These nonideali-ties include sudden rise and fall in supercapacitor voltage (see Fig. 7(d)) during state transitions (shown in Fig. 7(e)) due to the internal charge redistribution between different equivalent internal capacitors [26], [27].
In summary, through experimental validation of the pro-posed REC circuit model in this section, we have motivated the need for the analysis of practical supercapacitor models.
VI. SIMULATION MODEL FOR REC CHARACTERIZATION, ITS ANALYTICAL VERIFICATION, AND RESULTS
A. SIMULATION MODEL
As discussed in Section IV-A, to deal with the REC characterization of modern supercapacitor models that are analytically-intractable, we have developed a generic simula-tion framework. This proposed simulasimula-tion model can provide RF charging and loading times for practical supercapacitor model with any level of complexity in design.
The simulation model provides voltage and current numer-ical values as a function of time, which can be stored in the iDEM memory for estimating the charging time TC and
revisit (loading) time TL based on the values of VH and VL. Although there is no closed-form expressions of TC and TL
available for highly complex but realistic models, this simula-tion model, which incurs one-time computasimula-tion cost, provides
an accurate estimate of the charging time and node lifetime. We have used the trapezoidal rule, which is based on the principle of approximating the region under the graph of the integrand as a trapezoid and then calculating its area. Voltage across supercapacitor VC(t) at time t can be approximated as:
1 C Z t t0 I(τ) dτ +VC(t0)≈ t − t0 2C [I(t)+I (t0)]+VC(t0) . (23) The simulation flow given in Fig. 8 involves 3 steps: • Initializationof voltage across the capacitor(s) and
resis-tor(s) at time t = 0 along with the branch current values. • Recursion, which involves the usage of update equations for deriving voltage and current expressions for the nth time instant using the current and voltage expressions at n −1 and n − 2 time instants. Here, tn− tn−1=1t 1 is the step size used in the simulation. The initialization and update equations for constant-power charging and CPL for various supercapacitor models are respectively given in Table 3 and Table 4. In the simulation model, 1t = 0.05 sec, t0=0 sec, and initial update for t =1t is found by using the initial (t = t0) current and voltage values. The equations mentioned in Tables 3 and 4 are obtained using the KVL equations given in Section IV, approximation (23), basic circuit laws, and by solving polynomial equation of second degree to find I (t). • Termination, when t = TC(respectively, t = TL) while
RF charging (respectively, loading).
FIGURE 8. Simulation flow.
B. ANALYTICAL VERIFICATION AND SIMULATION RESULTS The accuracy of the simulation model in estimating the charging time and loading time is validated for the superca-pacitor models (ideal, commercial, simplified, and 1-branch) that have the closed-form analytical expressions. Figs. 9 and 10(a) show that the charging time TC variation with P = 0.12 W obtained from the proposed simulation model closely matches the analytical equations developed in Section IV-A. Root mean square error (RMSE) of the analytical RF charging equations with respect to the results obtained from the simulation model for ideal, commercial, simplified, and 1-branch models are respectively 0.0797, 0.0727, 0.0691, and 0.0573, which are within the allow-able upper limit of 0.08 for a model to be considered as good fit [39]. In the same figures, the proposed simulation model is also used for deriving loading and charging time for analytically-intractable 3-branch model. These values are utilized in estimating the sustainable network size for perpetual operation in the next section. Fig. 10(a) also plots the energy stored in various branches of 3-branch model,
FIGURE 9. RF charging of 4.7 F supercapacitor (cf. Table 2).
FIGURE 10. RF charging of 50 F supercapacitor (cf. Table 2). (a) Capacitor voltage variation. (b) Charging current variation.
which illustrates that most of the energy is stored in the first branch (C1and Cv), followed by the second branch.
Figs. 10(b) show the charging current I (t) versus time. As shown in Fig. 10(b), the current across the second and third branches (I2(t) and I3(t)) in 3-branch model along with IRle(t) across the leakage resistor Rle in 1-branch
and 3-branch models increase with time. However, for t > 800 sec, I2(t) decreases with time because the charge starts to get accumulated in the delayed branch also [26], [27].
Figs. 11(a) and 11(b) show the charging time TC
vari-ation in different supercapacitor models with VL = 2 V, VH =2.5 V, and P varied as 0.12 W, 0.055 W, and 0.025 W for different iDEM recharging distance: 45 cm, 66 cm, and 100 cm. The performance of simplified, practical 1-branch, and 3-branch models incorporate the long-term behavior very differently from the ideal and commercial models. For
exam-TABLE 3. Constant-power charging initialization and update equations.
TABLE 4. Constant-power loading initialization and update equations.
ple, TC for ideal model is respectively 50.47% and 30.47% lesser than the practical 3-branch model in 4.7 F and 50 F supercapacitors.
Figs. 12(a) and 12(b) plot the variation of capacitor voltage and loading current I with time for P = 0.12 W. The results
from the developed simulation model closely match with that analytically obtained using duality principle (Section IV-B). RMSE of 0.0358, 0.0177, 0.0183, and 0.0268, respectively in TL values obtained from analytical equations and
FIGURE 11. RF charging and constant-power loading time comparison. (a) TCfor 4.7 F. (b) TCfor 50 F. (c) TLfor 4.7 F. (b) TLfor 50 F.
FIGURE 12. Constant-power loading of 4.7F supercapacitor (cf. Table 2). (a) Capacitor voltage variation. (b) Current variation.
FIGURE 13. Constant-power loading of 50 F supercapacitor (cf. Table 2). (a) Capacitor voltage variation. (b) Current and power variation.
models, validate that the proposed simulation model is a good fit [39] with the analytical expressions derived for both TLand TC.
Next we show the impact of state-dependent energy con-sumption of a field node. Figs. 13(a) shows the tempo-ral variation capacitor voltage (VC(t) or VC1(t)) with 50 F supercapacitor for 1-branch and 3-branch models along
FIGURE 14. Simulation results for energy distribution. (a) Component contribution. (b) Utilization factor. (c) Distribution for 50 F.
with the energy stored Epr1b
s1 = 1 2 C1+ CvVC V 2 C and Epr3b s1 = 1 2 C1+ CvVC1 V2 C1
in the first branch for both instantaneous and average power consumption scenarios. After t = 600 sec, the load is removed from the circuit to show the leakage and self-discharge effects (cf. Fig. 13(a)). The temporal variation of loading current I (t) (for 1-branch model) and power P for each sensor are shown in Fig. 13(b). As shown in Fig. 13(a) the state-dependent average and instantaneous (or variable) power consumptions has approx-imately the same nature after t = 600 sec, which implies that P = Pavgconscan be considered during CPL-based node lifetime
estimation.
Figs. 11(c) and 11(d) show the loading time TL
varia-tion for different supercapacitor models with VL = 2 V, VH = 2.5 V, and P = 0.7n mW, where n is the number of sensors per node (calculated using the consumption model given in Section III-B.2). The results show that, TL for 3-branch model are respectively 85.24% and 28.80% lesser than the TL obtained using the ideal model with 4.7 F and 50 F supercapacitors – which are very significant differences.
Effective energy utilization is one of the major fac-tors affecting the performance of energy harvesting nodes. In Fig. 14(a), the distribution of energy among different capacitors in the 3-branch model with varying dstop values
shows that most of the energy is stored in the first branch. The utilization factor UF = Estored
Estored+Elost along with Estoredfor different models in Fig. 14(b) show that, UF with ideal and commercial models are almost 1, whereas for 3-branch model it is less than 0.5. Fig. 14(c) presents the distribution of total supplied energy Esuppin 3-branch model, which indicates that
the practical supercapacitors suffer from significant energy loss (about 50%) due to leakage. This can have a significant impact on perpetual network operation, as explained next.
VII. ESTIMATION OF SUSTAINABLE NETWORK SIZE
We now use the results on charging and discharging char-acteristics to find the RFEH-assisted pollution monitoring network size that can be supported by a single iDEM for uninterrupted operation. Network size is defined as follows:
Definition 6: Network size is defined as the number of field nodes that can be served in a manner that none of the nodes ever runs out of energy or buffer space.
Here, energy depletion is more critical because a node becomes nonfunctional if its energy level goes below Emin.
Based on the consumption in different operational states of a field node (Section III-B.2) and the expressions of TCand TL(Section VI), we obtain the lifetime of each node
in the network. Using the node lifetime along with TC and
inter-node travel time, the network size is estimated. Below, we discuss the network model parameters for the network size estimation.
A. NETWORK MODEL
Field nodes are deployed over a square 5 km × 5 km field of area following the Poisson point process (PPP). We have considered PPP for sensor node deployment because it is the most widely used mathematical model for analyzing the per-formance of wireless adhoc and sensor networks with random topologies [40]. The speed of iDEM is taken 5 m/s. The charg-ing time parameters taken from the experimental observations are: RF transmit power 3 W; operating frequency 915 MHz; transmitter and receiver antenna gains 6.1 dBi; supercapacitor value C = 50 F; VL = 2 V and VH = 2.5 V. The different cases considered are:
1) Sensing-Dependent Energy Consumption of the Field Nodes: Due to sensing-dependent variable energy consumption, some field nodes may require more frequent replenishment than the others, and as a result the iDEM needs to visit such nodes more frequently. To implement this randomness of the field nodes’ energy consumption, we have considered three example cases:
Case A: All nodes consume nearly the same energy and have the same estimated revisit time; Case B: Some random-ness in energy consumption is present in the network, due to which some nodes’ consumption rate is about twice as
compared to the others; and Case C: Due to additional degree of randomness, the nodes are divided in 3 groups. The number of visits in a tour of iDEM are: one for group 1 nodes, two for group 2, and four for group 3. The three group sizes are equal in size and uniformly random distributed in space.
2) Stopping Distance dstop of iDEM From the Node to be Charged:Due to small RFET range, the three stopping dis-tances considered are: 45 cm, 66 cm and, 100 cm. This parameter determines TC, because the values of harvested
DC power P, calculated by considering Powercast P1110 RF-to-DC rectification efficiency [34] and path loss, for the three dstop values are 0.12 W, 0.055 W, and 0.025 W,
respectively.
3) Number of Sensors Per Node:(i) One sensor: CO having P = Pavgcons≈0.7 mW; (ii) Two sensors: CO and NO2having P = Pavgcons≈1.4 mW; (iii) Three sensors: CO, NO2, and H2S having P = Pavgcons ≈ 2.1 mW; (iv) Four sensors: CO, NO2, H2S, and SO2having P = Pavgcons ≈2.8 mW. This parameter
influences the CPL time TL.
4) Supercapacitor Models: Different models considered are: ideal, commercial, practical 1-branch and 3-branch models. Simplified model is not considered due to the unavailability of the corresponding circuit parameters for 50 F supercapacitor.
In order to serve the maximum number of nodes, iDEM should spend minimum time in traveling, i.e., the overall tour length should be minimized. In differential energy con-sumption scenarios, since conventional Traveling Salesman Problem (TSP)-based solutions cannot be used directly, three example TSP tours are considered: a) TSP tour 1 having only group 3 field nodes; b) TSP tour 2 having group 2 and 3 nodes; c) TSP tour 3 having nodes from all 3 groups. So, one complete schedule of iDEM will start TSP tour 1, followed by TSP tour 2, TSP tour 1, and finally TSP tour 3, so that group 1, 2, and 3nodes are served respectively once, twice, and four times in a single iDEM tour. The TSP tours are found using Genetic Algorithm. This iDEM schedule is then repeated, thus providing an uninterrupted network operation. Numerical results presented below are based on an average over 30 runs.
B. NUMERICAL RESULTS
Sustainable network size for different supercapacitor models under different degree of randomness in energy consumption are shown in Figs. 15, 16, and 17. The effect of recharging distance dstopon network size is shown in the respective
sub-figures (a), (b), and (c). The results show that the network size with practical supercapacitor models is very different from the ideal or commercial models. Using commercial, 1-branch, and 3-branch models, the average number of nodes served with different number of sensors per node, dstopvalues, and
energy consumption cases are respectively 1.52% 14.18%, and 52.20% less than what can be supported using the ideal model.
The impact of energy consumption diversity on the sustainable network size can be realized from the fact that, in
FIGURE 15. Case A: Only group 1 nodes. (a) dstop=45 cm. (b) dstop=66 cm. (c) dstop=100 cm.
FIGURE 16. Case B: Both group 1 and group 2 nodes. (a) dstop=45 cm. (b) dstop=66 cm. (c) dstop=100 cm.
FIGURE 17. Case C: All three group of nodes considered. (a) dstop=45 cm. (b) dstop=66 cm. (c) dstop=100 cm.
cases B and C (Figs. 16 and 17) the network size supported by a single iDEM are respectively 16% and 40% lesser than in case A (Fig. 15). The harvested DC power P for recharging a field node sharply reduces with the increased iDEM recharg-ing distance dstop, causing an increased RF charging time and
hence reduced sustainable network size. The average network size with dstopas 66 cm and 100 cm are respectively 48.61%
and 75.33% lesser than that with dstop=45 cm. Further, the
number of sensors per node also has a great impact on the network size. In networks with two, three, and four sensors per node, the network size is 54.01%, 72.14%, and 80.74% less as compared to the networks with single sensor per node. Table 5 shows that the average charging time TCis
compa-rable to the average traveling time for case C. In cases A and B with larger network size and lower degree of randomness in energy consumption, TC is much higher than the traveling
time, which is because, with increasing network size, the total charging time increases. The respective shares of TC in a
single iDEM tour schedule for cases A, B, and C are 86.98%, 73.90%, and 54.64%. The results show that, TC is a major
cost (more than 50%) that needs to be tackled in RFET-based
TABLE 5.iDEM scheduling numerical results.
energy replenishment techniques, as it plays a significant role in estimating the network size that can be supported by a single iDEM. Commercial and ideal supercapacitors have similar performances in terms of TC and sustainable
network size. However the performance of 1-branch and 3-branch models is very different. Also, the effect of leakage
and self-discharge leading to 50% energy loss is captured in TLexpression for practical supercapacitor models. The above
results signify the importance of accurately estimating the cir-cuit parameters and using the proposed RF charging and node lifetime formulations based on these practical supercapacitor models.
VIII. CONCLUDING REMARKS
In this work we have shown that the nonidealities in practical supercapacitors have significant impact on the performance of energy harvesting networks. To gain analytical insights on practical rechargeability constraints, REC circuit model has been proposed and RF charging time and node lifetime expressions for the practical supercapacitor models have been derived. The analytical circuit model for the REC has been validated through hardware experiments. Based on a dual-ity principle, constant-power loading time has been derived from the RF charging time characteristics of the practical supercapacitors. To deal with more practical but analyti-cally intractable supercapacitor models, a generic simulation model has been developed. The models developed for charg-ing and loadcharg-ing time have been used to find the sustainable network size for green perpetual network operation of an energy-hungry sensor network, such as, pollution monitoring network. With the help of analytical and numerical results presented in this paper, we show that the lifetime of a typical RFEH-assisted pollution monitoring network with current consumption model given in Table 1 gets reduced by 28.80% on accounting the nonidealities, such as, self-discharge, leak-age, and aging effects in practical supercapacitors. Further, the impact of leakage and aging effects of the practical super-capacitors for commercial wireless pollution monitoring field nodes with Mica2 mote, RF energy harvester, and antennas from Powercast demonstrate significant difference in terms of sustainable network size (e.g., 52% lesser network size with 3-branch model as compared to the ideal model) supported by a single iDEM.
The developed models and observations presented here will be useful in accurately planning and estimating the per-formance of green energy harvesting sensor networks.
APPENDIX A
CHARGING CURRENT VARIATION FOR 1-BRANCH MODEL
Applying KVL in Fig. 4(d) and using VC(t = 0) = 0, gives:
h IRle(t)Rle− I1(t)R1 i ·C1+ Cv· VC(t) = Z t 0 I1(t)dt (A.1) Using VC(t) = IP(t)− I1(t)R1, IRle(t) = I(t)RPle, I1(t) = I (t) − P
I(t)Rle, and differentiating (A.1) with respect to t, we obtain: (C1+2Y3) dI(t) dt R1+ PR1 [I (t)]2Rle + P I(t)2 = P I(t)Rle −I(t) (A.2) where Y3 = Cv P I(t)− R1 h I(t) −I(t)RP le i . Solving (A.2), the time Tpr1b
CI during which I (t) falls from I (t = 0) = q P(R1·Rle) R1+Rle to I Tpr1b CI = IL is: Tpr1b CI = 1 2Rle RleC1 (2R1+ Rle) ln PRle R1 IL2 Rle− P +(R1+ Rle) ln " I2 L Y4 #! −4Cv tanh−1 √ RleIL √ P −tanh−1 r RleY4 P !# q PR3le(2R1+ Rle) +P(R1+ Rle) 2 IL + R1Rle n Rle p Y4+ ILR1 o (A.3) where Y4=P(RR1+Rle)
1Rle . It may be noted that, T
pr1b
CI is a function of the current IL. Following the similar approach current variation with time for CPL can also be obtained.
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DEEPAK MISHRA (S’13) received the B.Tech. degree in electronics and communication engi-neering from Guru Gobind Singh Indraprastha University, Delhi, India, in 2012. He is currently pursuing the Ph.D. degree with the Department of Electrical Engineering, IIT Delhi, India. His research interests include RF energy harvesting cooperative communication networks and energy optimization schemes for uninterrupted operation of mobile ad hoc networks.
SWADES DE (S’02–M’04–SM’14) received the Ph.D. degree from the State University of New York at Buffalo, NY, USA, in 2004. In 2004, he was an ERCIM Researcher with ISTI-CNR, Italy. From 2004 to 2006, he was with NJIT as an Assistant Professor. He is currently an Associate Professor with the Department of Electrical Engi-neering, IIT Delhi, India. His research interests include performance study, resource efficiency in wireless networks, broadband wireless access, and optical communication systems.
